It is a primary object of the present invention to provide a heat exchanger of the above-described type which is economical to manufacture and which has a high operating efficiency in that the heat transfer through the plates forming the flow passages for the first fluid between the first fluid inlet openings and the first fluid outlet openings and forming the flow passages for the second fluid between the second fluid inlet openings and the second fluid outlet openings is optimised, thereby achieving a high rate of heat transfer from the first fluid to the second fluid.